Answer:
$1032.60
Step-by-step explanation:
Given data
salary = $950 every two weeks
tax rate = 8%
let the initial pay be x
and let the pay after tax deduction be p
p= x-8/100x
Hence the equation for his pay is
subsitute
950=x-0.08x
950= 0.92x
divide both sides by 0.92
x= 950/0.92
x=$1032.60
The employee make $1032.60 every two weeks before taxes
Parameterize by the vector function
so that the normal vector to is given by
with magnitude
In this case, the normal vector is
with magnitude . The integral of
over
is then
where is the region in the
plane over which
is defined. In this case, it's the triangle in the plane
which we can capture with
and
, so that we have
<u>Answer:</u>
The probability of a randomly selected student scoring in between 77.6 and 88.4 is 0.8185.
<u>Solution:</u>
Given, Scores on a test are normally distributed with a mean of 81.2
And a standard deviation of 3.6.
We have to find What is the probability of a randomly selected student scoring between 77.6 and 88.4?
For that we are going to subtract probability of getting more than 88.4 from probability of getting more than 77.6
Now probability of getting more than 88.4 = 1 - area of z – score of 88.4
So, probability of getting more than 88.4 = 1 – area of z- score(2)
= 1 – 0.9772 [using z table values]
= 0.0228.
Now probability of getting more than 77.6 = 1 - area of z – score of 77.6
So, probability of getting more than 77.6 = 1 – area of z- score(-1)
= 1 – 0.1587 [Using z table values]
= 0.8413
Now, probability of getting in between 77.6 and 88.4 = 0.8413 – 0.0228 = 0.8185
Hence, the probability of a randomly selected student getting in between 77.6 and 88.4 is 0.8185.
Given:
The function is
where, function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.
To find:
Number of complex and real zeros.
Time intervals for which the population increased and population deceased.
Solution:
We have,
Here, degree of function x is 3. It means, the given function has 3 zeros.
From the given graph it is clear that, the graph of function r(x) intersect x-axis at once.
So, the given function r(x) has only one real root and other two real roots are complex.
Therefore, function r has 2 complex zeros and one real zero.
Before x=6, the graph of r(x) is below the x-axis and after that the graph of r(x) is above the x-axis.
Negative values of r(x) represents the decrease in population and positive value of r(x) represents the increase in population.
Therefore, based on instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.